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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 4, Pages 91–164 (Mi izv4278)  

This article is cited in 11 scientific papers (total in 12 papers)

Harmonic analysis on local fields and adelic spaces. II

D. V. Osipov, A. N. Parshin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We develop harmonic analysis in certain categories of filtered Abelian groups and vector spaces. The objects of these categories include local fields and adelic spaces arising from arithmetic surfaces. We prove some structure theorems for quotients of the adèle groups of algebraic and arithmetic surfaces.

Keywords: arithmetic surfaces, higher adèles, harmonic analysis, Fourier transform, Poisson summation formulae.

DOI: https://doi.org/10.4213/im4278

Full text: PDF file (1057 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2011, 75:4, 749–814

Bibliographic databases:

Document Type: Article
UDC: 512.75
MSC: 11R56, 18B30, 43A70
Received: 22.12.2009
Revised: 10.12.2010

Citation: D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II”, Izv. RAN. Ser. Mat., 75:4 (2011), 91–164; Izv. Math., 75:4 (2011), 749–814

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    This publication is cited in the following articles:
    1. A. N. Parshin, “Notes on the Poisson formula”, St. Petersburg Math. J., 23:5 (2012), 781–818  mathnet  crossref  mathscinet  isi  elib  elib
    2. Previdi L., “Locally compact objects in exact categories”, Internat. J. Math., 22:12 (2011), 1787–1821  crossref  mathscinet  zmath  isi  elib  scopus
    3. Osipov D.V., Parshin A.N., “Harmonic analysis and the Riemann-Roch theorem”, Dokl. Math., 84:3 (2011), 826–829  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. D. V. Osipov, “The unramified two-dimensional Langlands correspondence”, Izv. Math., 77:4 (2013), 714–741  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. A. Cámara, “Locally convex structures on higher local fields”, J. Number Theory, 143 (2014), 185–213  crossref  mathscinet  zmath  isi  scopus
    7. Ivan Fesenko, “Geometric adeles and the Riemann–Roch theorem for $1$-cycles on surfaces”, Mosc. Math. J., 15:3 (2015), 435–453  mathnet  mathscinet
    8. D. V. Osipov, A. N. Parshin, “Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields”, Proc. Steklov Inst. Math., 292 (2016), 185–201  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Liu D., “Residues and duality on semi-local two-dimensional adeles”, J. Algebra, 448 (2016), 74–83  crossref  mathscinet  zmath  isi  elib  scopus
    10. Liu D., Zhu Y., “Lca(2), Weil Index, and Product Formula”, Adv. Math., 329 (2018), 1088–1136  crossref  mathscinet  zmath  isi  scopus
    11. D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Math. J., 30 (2019), 111–122  mathnet  crossref  isi  elib
    12. D. V. Osipov, “Arithmetic surfaces and adelic quotient groups”, Izv. Math., 82:4 (2018), 817–836  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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